arXiv:1306.1841 Abstract | arXiv Analytics

arXiv:1306.1841 [math.AP]Abstract References Reviews Resources

Isoperimetric inequality, $Q$-curvature and $A_p$ weights

Published 2013-06-07Version 1

A well known question in differential geometry is to control the constant in isoperimetric inequality by intrinsic curvature conditions. In dimension 2, the constant can be controlled by the integral of the positive part of the Gaussian curvature. In this paper, we showed that on simply connected conformal flat manifolds of higher dimensions, the role of the Gaussian curvature can be replaced by the Branson $Q$- curvature. We achieve this by exploring the relationship between $A_p$ weights and integrals of the Q-curvature.

Comments: 19 pages

Categories: math.AP, math.DG

Subjects: 52B60, 42B35

Keywords: isoperimetric inequality, gaussian curvature, simply connected conformal flat manifolds, intrinsic curvature conditions, differential geometry

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